In recent years, the Adaptive Antoulas-Anderson (AAA) algorithm has been applied extensively for generating Reduced Order Models (ROMs) of large scale Linear Time-Invariant systems starting from measurements of their transfer functions. When used for Model Order Reduction (MOR) of an asymptotically stable system, the ROMs generated applying AAA are not guaranteed to preserve this fundamental property, thus rendering them impractical in many relevant applications. To overcome this issue, we propose a novel algebraic characterization for the stability of ROMs represented under the AAA barycentric structure. We then translate such characterization into a set of convex semidefinite constraints that can be embedded into the AAA optimization routine to explicitly maximize the model accuracy while ensuring its stability. Finally, we generalize the resulting modeling framework to allow for efficient stable MOR of Multi-Input-Multi-Output systems. An extensive set of numerical experiments provides practical evidence for the effectiveness of the proposed approach and compares its performance with those of available state-of-the-art methods.
